J. Am. Chem. SOC.1995, 117, 10389-10390
10389
New Principle for the Determination of Coupling Constants That Largely Suppresses Differential Relaxation Effects A. Rexroth,+ P. Schmidt? S. Szalma,g T. Geppert,+ H. Schwalbe," and C. Griesinger*.+ Institut f i r Organische Chemie, Universitat Frankfurt Marie Curie-Strasse 11, 0-60439 Frankfurt, Germany Biosym Technologies Inc., 9685 Scranton Road San Diego, Califomia 92121-3752 Department of BCPM, Harvard Medical School 240 Longwood Avenue, Boston, Massachusetts 02115 New Chemistry Laboratory, University of Oxford South Parks Road, Oxford OX1 3QT, U.K. Received May 23, I995
The determination of coupling constants in biomacromolecules provides information about local conformations and complements the structural information obtained from NOES.' A number of different methods for the determination of coupling constants have been introduced over the years. Among these are E.COSY-derived methods,2 methods relying on fitting procedures," and techniques based on quantitative J correlat i o n ~ . ~All . ~these methods either measure directly or let evolve during a limited amount of time a relatively small coupling constant (-10 Hz) of interest. Due to the faster relaxation of antiphase terms compared to in-phase terms, the observed value Jeff tends to be smaller than the actual coupling constant JS6 This effect is also known as scalar relaxation of the second kind.7 From the formula derived for differential relaxation6 and its Taylor series expansion one obtains for J >> Apl2n
where Ap is the difference of the relaxation times for antiphase and in-phase transverse coherences. Since the absolute error of J, ( J - Pff),is inversely proportional to J, the larger J, the smaller the error due to differential relaxation. Since coupling constants cannot be
* To whom correspondence should be addressed. Universitat Frankfurt.
* Harvard Medical School. +
Biosym Technologies Inc. 'I University of Oxford. (1) Neri, D.; Szyperski, T.; Otting, G.; Senn, H.; Wiithrich, K. Eiochemi s m 1989.28, 75 11. Garrett, D. S.;Kuszewski, J.; Hancock, T. J.; Lodi, P. J.; Vuister, G. W.; Gronenbom, A. M.; Clore, G. M. J. Magn. Reson. E 1994,104, 99. Karimi-Nejad, Y.; Schmidt, J. M.; Riiterjans, H.; Schwalbe, H.; Griesinger, C. Biochemistry 1994, 33, 5481. (2) Griesinger, C.; Sorensen, 0. W.; Emst, R. R. J. Am. Chem. SOC.1985, 107, 6394. Griesinger, C.; Sorensen, 0. W.; Emst, R. R. J. Chem. Phys. 1986, 85, 6837. Griesinger, C.; Sorensen, 0. W.; Emst, R. R. J. M a p . Reson. 1987, 75, 474. (3) Keeler, J.; Neuhaus, D.; Titman, J. J. Chem. Phys. Lett. 1988, 146, 545. Keeler, J.; Neuhaus, D.; Titman, J. J. J. Magn. Reson. 1989, 85, 111. Keeler, J.; Titman, J. J. J. Magn. Reson. 1990, 89, 640. Schwalbe, H.; Samstag, W.; Engels, J. W.; Bermel, W.; Griesinger, C. J. Eiomol. NMR 1993,3,479. Schwalbe, H.; Marino, J. P.; King, G. C.; Wechselberger, R.; Bermel, W.; Griesinger, C. J. Eiomol. NMR 1994, 4 , 631. (4)Blake, P. R.; Summers, M. F.; Adams, M. W. W.; Park, J.-B.; Bax, A. J. Biomoi. NMR 1992.2, 527. Bax, A,; Max, D.: Zax, D. J. Am. Chem. SOC.1992, 114, 6924. Vuister, G. W.; Yamazaki, T.; Torchia, D. A,; Bax, A. J. Eiomol. NMR 1993, 3, 297. Vuister, G. W.; Wang, A. C.; Bax, A. J. Am. Chem. SOC.1993, 115, 5334. Grzesiek, S.; Vuister, G. W.; Bax, A. J. Eiomol. NMR 1993, 3, 487. Zhu, G.; Bax, A. J. Magn. Reson. 1993, 104, 353. Vuister, G. W.; Bax, A. J. Magn. Reson. B 1993, 102, 228. (5)Vuister, G. W.; Bax, A. J. Am. Chem. SOC.1993, 11.5, 7772. (6) Harbison, G. S . J. Am. Chem. SOC.1993, 115, 3026. Norwood, T. J. J. M a p . Reson. A 1993,104, 106. Norwood, T. J. J. Magn. Reson. A 1993, 101, 109. Schmidt, P.; Schwalbe, H.; Griesinger, C. 35th ENC, Poster WP 114, Asilomar, CA, 1994. (7) Abragam, A. Principles of. Nuclear Magnetism; Clarendon Press: . Oxford, 1961. 0
Figure 1. (a) Schematic representation of an E.COSY pattem for a three-spin system A, B, C, in which A is correlated with B and the interesting J(B,C) coupling can be measured in 0 2 due to the resolution of the submultiplet components by J(A,C) in 01. (b) Schematic representation of a DQ/ZQ experiment in which the sum Jz and the difference JAof J(A,C) and J(B,C) are used to extract J(B,C) from the difference of the splittings in the two spectra. (c) In DQ/ZQ+SQ-HNCA a doublet of doublets is observed yielding 3J(HN,H,) and 3J(HN,C,3) couplings as indicated. IH
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Figure 2. Pulse sequence for the determination of the 3J(HN,H,) coupling constant in a 3D DQ/ZQ+SQ-HNCA experiment. The 2D version ( t 2 = 0) was recorded with the following parameters: The I5N spins were decoupled using the CARPI4 sequence during f 3 . The delays were A = 5.2 ms, t = 13.7 ms, t' = 13.5 ms, 6 = 1.3 ms, 6' = 0.55 ms, E = 2.303 ms, = 34 p s (=duration of 180°(15N) tl(0)).The phase cycling employed for the sum of DQ and ZQ (difference of DQ and ZQ) is as follows: 41 = y , y , -y, -y; 42 = x , -x (y, -y); 43 = x , -x (y, -y); q P = x , x , -x, -1. The two sets (DQ+ZQ and DQZQ) were stored separately. States-TPPII5 on 43; eight FIDs for each set of DQ+ZQ and DQ-ZQ experiment and tl value; 200 tl values, spectral width in o ] ,0 2 4167 Hz, 4 kHz; 2048 complex points in f2. The duration, strengths of the gradients, and phase q were as follows: GI = (3.8 ms, i: 49.5 G/cm, 300 pus recovery), G2 = (1.8 ms, 10.1 G/cm, 200ps recovery), q = izy. For the 3D version, t 2 is incremented for 15N chemical shift evolution. For the DQ/ZQ+SQ version, K = 1 is recommended.
